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Decreasing basically means lowering or going down. Suppose you are driving above the speed limit; you should slow down. Students always want that their teachers decrease the number of tasks. The decrease is the opposite of growth. Simply, increase means higher, and decrease means lower.
The percentage decrease formula is a measure of how much a variable has lost its value. The variable can be population, cost, profit, etc. Percentage decrease refers to the percentage change in value when it decreases over a period of time. For example, a decrease in rainfall levels, a decrease in the number of covid patients, etc. Percentage decrease can be calculated using the percentage decrease formula. In this section, we will discuss the percentage decrease formula. Let's learn the percentage decrease formula with a few solved examples.
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Key Terms: Percentage, Percentage Change, Percentage Decrease, Percentage Decrease Formula, Percentage Increase, Ratio, Number, Denominator
What is Percentage Change?
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Change happens every day. Percentage means within 100, and percentage increase/decrease is only a variable change which is expressed as a percentage. As such one day, the temperature can be nice and warm, and you wear a shirt and shorts. But the next day can be cold, and you wear your grandmother's sweater with pants. Businesses, significant changes, such as one-year fewer sales than the previous year, are needed to be analyzed.
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How to Calculate the Percentage Change?
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We first start by calculating the total first and then compare it with the second total. For example, if we analyze the change in sales from one year to the next, our first total would be one year's sales, and our second total would be next year's sales. Then, we will determine if there is an increase or decrease. For example, if the second total is greater than the first, we have an increase, and if the second total is less than the first, we have a decrease.
After determining whether the change is increasing or decreasing, we calculate the change by subtracting the smaller from the larger. Then we divide it by the first total and to find the percentage, we then multiply by 100.
We can write a simple formula for decreasing percentage as
(decrease) / (first total) * 100.
No matter what problem we are given, until we are able to first find out the total and the amount of increase or decrease, then we can calculate the percentage increase or decrease.
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What is Percentage Decrease Formula?
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The percentage decrease formula reduces the quantity relative to its initial value. To calculate the percentage decrease, we first need to find the difference in values. Then, divide the difference by the starting value and multiply it by 100. The formula for percentage decrease is as given below:
Percent Decrease = [(Old Value - New Value) / Old Value] × 100]
This formula for percentage reduction will help solve a number of questions. Below are some important questions related to this formula.
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How to Calculate Percentage Decrease Formula
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There are three simple steps to calculate the percentage decrease using the percentage decrease formula, they are:
- Step 1: Find out the decreased value from the numbers, i.e.,
Decrease = OldValue – NewValue
- Step 2: Divide the difference by the old value, i.e.,
(OldValue - NewValue) / Old value.
- Step 3: Multiply that value by 100. This makes the percent decrease formula,
Percentage Decrease
= [(Old Value - New Value) / Old Value] × 100]
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Things to Remember
- The percentage is a ratio or number for measuring the value ratio, where the value is always 100.
- 100 is always the denominator and it is represented by the ‘%’ symbol.
- Percentage calculation means finding the whole number in terms of 100.
- The percentage decrease formula is Percentage Decrease = (Decrease in Value/ Old Value) x 100
Sample Questions
Ques. A shopkeeper used to sell a pair of pens for Rs. 25. He then reduced the price of the same pair of pens to Rs. 21. Calculate the percentage decrease in cost. (2 marks)
Ans. Now, the decrease amount is = Rs. (25 – 21) = Rs. 4
Hence, the decrease in percentage = (4/ 25) × 100 = 16%
Ques. A shopkeeper sells a pair of pens for Rs. 30 initially. He then reduced the price of the pair of pens to Rs. 24. Calculate the Percentage Decrease in the cost of pens? (2 marks)
Ans. Now, the decrease amount is = Rs. (30 – 24) = Rs. 6
Hence, the decrease in percentage = (6/ 30) × 100 = 20%
Ques. Price of Sugar Decreases from Rs. 9 to Rs. 7.5 per Kg? What is the Percentage Decrease in the Price of Sugar? (2 marks)
Ans. Now, the decrease amount is = Rs. (9 – 7.5) = Rs. 1.5
Hence, the decrease in percentage = (1.5/ 9) × 100 = 16.66%
Ques. The number of illiterate persons in a country decreased from 150 lakhs to 100 lakhs in 10 years. What is the percentage of decrease? (2 marks)
Ans. Now, the decrease amount is = Rs. (150 – 100) lakh = Rs. 50 lakhs
Hence, the decrease in percentage = (50/ 150) × 100 = 3313%
Ques. A fruit seller used to sell bananas for Rs. 40 per dozen. Now he reduced the cost of a dozen bananas by 10%. What is the price of a dozen bananas now? (3 marks)
Ans. Let assume, the new value for a dozen bananas is Rs. x.
Now, Decrease Value = Rs. (40 – x)
According to the Percent Decrease Formula,
Percentage Decrease = (Decrease Value/ Old value) × 100
⇒ 10 = [(40 – x)/40] * 100
⇒ 10/100 = (40 – x)/40
⇒ 40 – x = 4
⇒ x = 36
Hence, the new price of a dozen of bananas is Rs. 36.
Ques. A fruit seller used to sell bananas for Rs. 30 per dozen. Later, he reduced the cost of a dozen bananas by 15%. Find the price of a dozen bananas now? (3 marks)
Ans. Let’s assume, the new value for a dozen bananas is Rs. x.
Now, Decrease Value = Rs. (30 – x)
According to the Percent Decrease Formula,
Percentage Decrease = (Decrease Value/ Old value) × 100
⇒ 15 = [(30 – x)/30] * 100
⇒ 15/100 = (30 – x)/30
⇒ 30 – x = 9/2
⇒ x = 30 – 4.5
⇒ x = 25.5
Hence, the new price of a dozen of bananas is Rs. 20.
Ques. The cost of a membership card of a club was reduced by 20% and costs Rs. 550 now. What was the original price of the membership card before its cost was reduced? (5 marks)
Ans. Let’s assume, the original cost was Rs. x.
Now, Decrease Value = Rs. (x – 550)
According to the Percent Decrease Formula,
Percentage Decrease = (Decrease Value/ Old value) × 100
⇒ 20 = [(x – 550)/x] * 100
⇒ 20/100 = (x – 550)/x
⇒ 5x – 2750 = x
⇒ 4x = 2750
⇒ x = 687.5
Hence, the original price of the membership card was Rs. 687.5.
Ques. The number 53 is misread as 35. Find the percent decrease using the percent decrease formula. (3 marks)
Ans. Now, the new value = 35 and the old value = 53
According to the Percent decrease formula,
Percent Decrease = [(Old Value – New Value) / Old Value] × 100
= [(53 – 35)/53] × 100
= 18/53 × 100
= 33.9%
Hence, the percent decrease of the number is approximately 34%
Ques. An article whose CP is Rs. 250 was sold for Rs. 230. Use the percent decrease formula to find the percent decrease in the price of the article. (3 marks)
Ans. Now, the new value = Rs. 230 and the old value = Rs. 250
According to the Percent decrease formula, we get
Percent Decrease = [(Old Value – New Value) / Old Value] × 100
= [(250 – 230)/250] × 100
= 20/250 × 100
= 8%
Hence, the percentage decrease in the price of the article is 8%.
Ques. A fruit seller used to sell strawberries for Rs. 80 per dozen. Now, he reduced the cost of a dozen strawberries by 5%. What is the price of a dozen strawberries now? Calculate by using the percent decrease formula. (3 marks)
Ans. Let’s assume, the new value for a dozen strawberries is x.
According to the percent decrease formula,
Percent Decrease = [(Old Value - New Value) / Old Value] × 100
⇒ 5 = [(80 – x)/80] × 100
⇒ 5/100 = (80 – x)/80
⇒ 80 – x = 4
⇒ x = 76
Hence, the new price of a dozen of strawberries is Rs. 76.
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